Dr Richard Earl, Worcester College, University of Oxford
Through the 19th century and into the 20th, mathematicians began increasingly to uncover surprises (some nice, some nasty) amongst their notions of geometry and space. Seemingly axiomatic ideas like the parallel postulate, crucial notions such dimension and volume were, all of a sudden, much less certain than had been previously been the case. This talk covers some of those seminal discoveries with a focus mainly on the Banach-Tarski paradox which states that, by means of breaking an object into finitely many pieces, its volume can be doubled; reassuringly (or perhaps not!) this is not the case with area.